Related papers: H-infinity and Complex Interpolation
We study in this article a possible further structure of homotopic nature on multiplicative spectral sequences. More precisely, since Kadeishvili's theorem asserts that, given a dg (or A-infinity-)algebra, its cohomology has also a…
We establish a simple, explicit relation between the formalisms employed in the treatments of polarization observables in deuteron two-body electrodisintegration published by Arenh\"ovel, Leidemann, and Tomusiak in Few-Body Systems {\bf…
In this paper, we study the H\"older-type interpolation inequality and observability inequality from measurable sets in time for parabolic equations either with L^p unbounded potentials or with electric potentials. The parabolic equations…
We consider K-interpolation methods involving slowly varying functions. Let $\overline{A}_{\theta,*}^{\mathcal{L}}$ and $\overline{A}_{\theta,*}^{\mathcal{R}}$ $(0\leq\theta\leq1)$ be the so called ${\mathcal{L}}$ or ${\mathcal{R}}$…
This paper is withdrawn due to copyright restrictions. The final version will become available at this url: http://pubs.acs.org/journals/jpcbfh/
Goedel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the…
This is a report on the recent work "Mirror symmetry for exceptional unimodular singularities" joint with Changzheng Li, Si Li and Yefeng Shen.
This paper has two purposes. The first is to explicate the diagrammatic approach to Hopf algebras due to Kuperberg, and to examine his proof of the existence and uniqueness of integrals in both the diagrammatic and purely algebraic…
This preprint was split in two and became the first two parts of a four-part series (arXiv:1405.1956, arXiv:1405:1955, and two in preparation). The remaining relevance of this preprint is due to the series of videotaped lectures (wClips)…
H\"older estimates and Harnack inequalities are studied for fully nonlinear integro-differential equations under some mild assumptions. We allow the kernels of variable order and critically close to 2.
The real and complex interpolation spaces for the classical Hardy spaces $H^1$ and $H^\infty$ were determined in 1983 by P.W. Jones. Due to the analytic constraints the associated Marcinkiewicz decomposition gives rise to a delicate…
The purpose of this paper is to introduce into consideration an analogue of the concentration index in the class of subharmonic functions of infinite order. The one in the case of finite order is used in the interpolation theory.
This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…
We prove a filtered version of the Homotopy Transfer Theorem which gives an A-infinity algebra structure on any page of the spectral sequence associated to a filtered dg-algebra. We then develop various applications to the study of the…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
This is an English translation of the monograph "Die Klassenk\"orper der komplexen Multiplikation" by Max Deuring, published in 1958 as Enzyklop\"adie der Mathematischen Wissenschaften, Band I-2, Heft 10, Teil II by B.G. Teuber…
This is an updated survey on the inverse spectral problem written for the Notices of the ICCM. It rapidly reviews some of the material in the previous survey of the same title (arXiv:math/0402356) and then discusses some relatively new…
We prove the finiteness of crystalline cohomology of higher level. An important ingredient is a "higher de Rham complex" and a kind of Poincar\'e lemma for it.
We analyze the differential relation corresponding to integrability of almost complex structures, reformulated as a directed immersion relation by Demailly and Gaussier. Combining results of Clemente [3], we show that applying h-principle…